Low complexity frequency estimator and interference cancellation method and device

ABSTRACT

A method and apparatus for estimating the frequency of a periodic signal and for canceling the interference in a modem signal. Power line noise may interfere with electronic signals. Since power lines may be either 50 Hz or 60 Hz, depending on the country, frequency estimation of the periodic power line noise is necessary. Modem signals are received and autocorrelated in order to identify the periodic characteristics of the signal over time. Once the frequency is identified, the power line noise is modeled based on creating a circular buffer. Initially, the circular buffer is composed of scaled samples of one cycle of the fundamental frequency of the power line noise. Thereafter, samples are received, scaled, and combined with previous buffer values in order to update the buffer. In this manner, the buffer models the power line noise, so that the power line noise may be removed from the system.

REFERENCE TO RELATED APPLICATIONS

This application is a continuing application of U.S. application Ser. No. 09/050,736, filed on Mar. 30, 1998, now abandoned, U.S. application Ser. No. 09/087,625, filed on May 29, 1998, now abandoned, U.S. application Ser. No. 09/087,626, filed on May 29, 1998, now U.S. Pat. No. 5,903,615, claiming priority benefits under 35 U.S.C. §120.

NOTICE REGARDING COPYRIGHT

A portion of the disclosure of this patent document contains matter subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent disclosure document as it appears in the Patent and Trademark Office files and records but otherwise retains all copyrights whatsoever.

BACKGROUND OF THE INVENTION

The present invention relates to noise detection and, more particularly, to estimation and cancellation of noise in a system or device.

Electronic signals are often composed of a desired signal and noise. The noise may be considered anything undesirable that is included in the electronic signal. At times, the noise may interfere with the interpretation of the desired signal within the electronic signal. In order to interpret the desired signal with greater accuracy, the noise should be removed from, or reduced in, the electronic signal without significantly degrading the desired signal.

One example of a device that receives an electronic signal is a modem. A modem typically modulates information for transmission over a communication channel and demodulates signals received from the communication channel to recover information. Noise may corrupt the modulated signal, thereby degrading the desired signal, thereby requiring the use of noise reduction techniques to recover the desired signal. Other devices which are sensitive to noise include medical devices such as EKG monitors, audio systems, and industrial devices. For example, even though an electronic device is internally well-buffered, such as in the case of an EKG monitor, external power line noise can filter into the system, interrupting the desired signal. As another example, where a machining device has motion control as part of its feedback, the motion control may experience interference from power line noise due to the harsh environment of the machining device.

Moreover, some devices use power lines as the medium by which to send data. The interference from the power line in that instance may significantly interfere with the data communication. Further, other types of electronic signals, such as video signals, may experience a “hum” due to power line noise. In the case where the video signal must be precise, the “hum” may interfere with the video.

Noise in a system may be either periodic or non-periodic. One source of periodic noise is the interference from AC power lines. Power line noise is commonly either 50 Hz or 60 Hz, depending on the power convention for the particular country. This type of noise may effect an electronic device in various ways. A high speed modem, for example, may suffer from periodic power line interference from one of several sources. There could be power line noise carried on the phone line to which the modem is connected. There could also be noise from an insufficiently filtered power supply for either the modem itself or the host computer to which the modem is attached.

There are various approaches to reduce noise, and in particular periodic noise, on a system. Two known approaches involve filtering the noise. First, a simple high pass filter may be used. The filter is designed to pass frequencies in the range of the desired signal and to block other frequencies. Thus, this approach may not require that the filter be designed specifically for a known frequency (such as in the power line example of 50 Hz or 60 Hz). In the alternative, a narrow notch filter may be designed if one has a priori knowledge of the frequency of the periodic interference. Both of these approaches may be useful if the frequency of the periodic noise does not fall within the range of the desired signal.

In those instances that require knowledge of the frequency of noise, a method and apparatus may be required for determining the frequency of an interfering periodic signal. Techniques exist which are known in the art for estimating frequencies of periodic signals on a communication channel. These techniques often involve generating a power density spectrum from a data sequence, and then analyzing the spectrum to identify peaks. While these techniques are useful for analysis of an arbitrary spectrum, they may require a large amount of computation. It is desirable to minimize the computational demands of the noise reduction technique. Another known approach is to filter the data sequence using narrow bandpass filters, with one filter centered at each frequency in question, and then compare the amplitudes of the filter outputs. This may be simpler than generating the complete spectrum, but a simpler approach is still desirable.

Once the frequency of the periodic noise is determined, the noise should be reduced or eliminated. In the power line example, desired signals (audio, data communications, etc.) are often corrupted by periodic interference such as from 50/60 Hz power line noise. Various techniques for removing the interference from the signal have been developed, such as high-pass filtering, notch filtering, and adaptive noise cancellation techniques. These techniques are often inadequate for a number of reasons. First, the interference often contains harmonics that exist in the same frequency range as the signal, in which case high-pass filtering is not sufficient. Second, the frequency of the interfering signal may not be known exactly, in which case a notch filter is not acceptable. Third, adaptive noise cancellation techniques typically require a reference which consists of the interference alone without the signal. In many cases, such a reference is unavailable. Fourth, the noise cancellation techniques often treat the periodic noise and the non-periodic desired signal in the same manner causing, in many instances, the desired signal to degrade when attempting to eliminate the noise within the system. For example, a notch filter, which is set at 60 Hz, treats the periodic noise and any desired signal component at 60 Hz equally, so that the desired signal may also be degraded.

A high speed modem is one example of a device that may suffer from periodic interference. Such interference will likely have harmonics throughout the frequency range of the modulated signal. As a further complication, the frequency of the periodic interference may be known approximately but not exactly. In addition, there will typically not be an interference reference available. Accordingly it is desirable to have an improved frequency estimator and interference cancellation method and apparatus.

SUMMARY OF THE INVENTION

In a first aspect of the invention, a method and apparatus is provided for identifying the frequency of a periodic signal within an electronic signal by treating the periodic signal as the primary signal and by treating the remaining portion of the electronic signal as background noise, uncorrelated with the periodic signal.

In a second aspect of the invention, a method and apparatus is provided for modeling and reducing periodic noise from an electronic signal. The periodic noise is treated as the primary signal and the remaining portion of the electronic signal is treated as background noise, uncorrelated with the periodic signal.

It is an object of the present invention to provide a method and apparatus for determining the frequency of a periodic signal.

It is a further object of the present invention to provide a method and apparatus for removing periodic interference, such as power line noise, from an electronic signal.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic representation of a data communication system.

FIG. 2 is a block diagram of a frequency estimation system in accordance with a preferred embodiment of the present invention.

FIG. 3a is a block diagram of a periodic interference cancellation system in accordance with a preferred embodiment of the present invention, which system is operable in a feed-back mode.

FIG. 3b is a block diagram of a periodic interference cancellation system, which system is operable in a feed-forward mode.

FIG. 4 is a block diagram of the signal integrator for generating the interference model, in accordance with a preferred embodiment of the present invention, for the interference estimator as shown in FIG. 3a or FIG. 3b.

FIG. 5 is a block diagram for correlating the received signal with the interference model, as shown in FIG. 4, to determine phase offset.

FIG. 6a is a block diagram of the interference canceller in the equalizer system of a pulse code modulated (PCM) modem.

FIG. 6b is a block diagram of the interference estimator as shown in FIG. 6a.

FIG. 7 is a block diagram of the interference canceller for a communication modem operating during echo canceller training.

DETAILED DESCRIPTION OF THE PRESENTLY PREFERRED EMBODIMENTS

Identification of a periodic signal (or signal components at discrete frequencies) within an electronic signal is often an important task in analyzing the electronic signal. One example of a periodic signal is periodic noise. Periodic noise may come from a variety of sources, such as via a power line. For instances in which the desired signal is spectrally flat (i.e., the desired signal has frequency components randomly distributed across some range), the periodic noise can be analyzed differently than the desired signal. In this manner, the periodic noise may be identified and eliminated more accurately and efficiently.

The presently preferred embodiments of the invention will now be described by reference to the accompanying figures, wherein like elements are referred to by like numerals. FIG. 1 is a schematic representation of a data communication system. A first data communications device 100 receives information 102 from a data source 104. The information 102 may be in either analog or digital form, although digital information is preferred for high speed data transfer applications. For instances in which the data communications device 100 receives information 102 from the data source 104 that is in analog form, the data communications device 100 may include an analog-to-digital converter that converts analog information 102 into digital form. Thus, the input to the communications device 100 may be in either analog or digital form, and the output of the communications device 100 is digital.

The first data communications device 100 is connected by a communication channel 106 to a second data communications device 108. The term modem may be used herein to refer to the data communications devices 100, 108. The communication channel 106 includes a digital telephone network (“DTN”) link 110 that is coupled to an analog subscriber loop 112 by a local switch 114. The DTN 110 carries digital information in the form of pulse code modulated (“PCM”) codewords, which are typically eight bits in length. The loop 112 carries an analog representation of the digital information. The local switch 114 acts as an interface between the DTN 110 and the loop 112 by converting digital information supplied by the DTN 110 into analog form for transmission over the loop 112 and converting analog signals supplied by the loop 112 into digital form for transmission over the DTN 110. The analog-to-digital and digital-to-analog conversions performed by the local switch 114 are well known conversions, such as the claw conversion that is utilized in North America and Japan or the European A-law conversion.

In a high speed data communication system, the data communications devices 100 and 108 process received data samples at rates of thousands of samples per second. In addition, with respect to the data communications device 108, periodic noise may be introduced to the received data samples from the analog subscriber loop 112, a power supply within the data communications device 108, a power supply within a host computer (not shown) connected to the data communications device 108, or any combination of the above sources. The data communication system shown in FIG. 1 may be utilized to download data from the device 100 to the device 108 at a rate of up to 56,000 bits/second in accordance with ITU-T Recommendation V.90, the contents of which are incorporated herein.

In accordance with a preferred embodiment, the frequency identification or estimation is performed during start-up operation of the electronic device, and in particular, the data communications device. However, if it is expected that the periodic frequency may change during a session of operation, the frequency estimation may alternatively be performed in the midst of steady state operation. If one performs frequency estimation during steady state operation, at such sample rates, there may not be time to do numerically intensive frequency detection methods, in addition to all of the other processing that the modem must perform between samples. Where one only needs to distinguish between two or more discrete frequencies or where one wishes to identify the frequency of a periodic signal, the following approach may be utilized.

In order to improve the performance of the data communications device, periodic noise should be reduced. To accomplish this, a frequency estimator, as described with reference to FIG. 2, is used to estimate the frequency of the power-line contributing to the noise. Moreover, an interference estimator, as described with reference to FIGS. 3 through 7, is used to model and reduce the noise contribution to the data communications signal. In accordance with a preferred embodiment, Appendix A includes source code for a frequency estimator. The code is written in assembly language for the Texas Instruments (TI) TMS32OC5x digital signal processor (“DSP”) platform.

Referring now to FIG. 2, for a system having a sample rate of f_(s), and two possible interfering frequencies f_(a) and f_(b), the length in samples of one cycle of the interfering frequencies is f_(s)/f_(a) and f_(s)/f_(b) respectively. For f_(s)=9600 samples/second, f_(a)=50 Hz, and f_(b)=60 Hz (i.e., the two typical frequencies for power line interference), these wavelengths would be: $\frac{f_{s}}{f_{a}} = {\frac{9600\quad {samples}\text{/}\sec}{50\quad {Hz}} = {192\quad {samples}}}$ $\frac{f_{s}}{f_{b}} = {\frac{9600\quad {samples}\text{/}\sec}{60\quad {Hz}} = {160\quad {{samples}.}}}$

The signal received by the modem is designated as x[k] where k is sample index. A sample index is a number used to identify a particular sample. If one uses a number in square brackets to denote the index, then the first sample is sample[0], the second sample is sample[1], and so on. By convention, it is common to have zero be the first index.

In order to determine which frequency is the source of the periodic interference, an autocorrelation method is used to identify the periodic characteristics of the received signal over time. The autocorrelation of the received signal x[k] is: ${R_{xx}(m)} = {\sum\limits_{k = 0}^{K - 1}{{x\lbrack k\rbrack} \cdot {x\left\lbrack {k - m} \right\rbrack}}}$

where K is the number of samples over which the autocorrelation is performed (i.e., from k=0 to K−1), and m is the offset. The optimum value for K is determined empirically. It has been determined that a value of K equal to the buffer length of 192 is sufficiently large to calculate R_(xx)(m) with confidence. However, a value of K much less than 160 may not work well in calculating a reliable R_(xx)(m) for comparison.

The incoming signal x[k] contains both the desired signal and the interference from the power line. As stated previously, the desired signal is assumed to be white in the absence of the interfering signal (i.e., the electronic signal is assumed random over time) or non-correlated to the interfering signal. Thus, the desired signal does not have to be gaussian white; it may simply be non-correlated to the power line noise. The interference, on the other hand, is assumed to be periodic so that the autocorrelation R_(xx)(m) will be large when m is an integer multiple of the wavelength of the interference, and small when m is some other value. Thus, the interference is treated differently than the desired signal due to the periodic nature of the interference. The interference may be thought of as being treated as the primary signal and the desired signal as the background noise.

The frequency of the periodic interference may be determined or identified by comparing R_(xx)( 192) (which corresponds to 50 Hz) and R_(xx)(160) (which corresponds to 60 Hz). The frequency corresponding to the larger autocorrelation is the frequency of the interference, i.e.: $f_{interference} = \left\{ \begin{matrix} {{{f_{a}\text{:}{{if}--}{R_{xx}\left( \frac{f_{s}}{f_{a}} \right)}}\rangle}{R_{xx}\left( \frac{f_{s}}{f_{b}} \right)}} \\ {{{f_{b}:{{{if}--}{R_{xx}\left( \frac{f_{s}}{f_{b}} \right)}}}\rangle}{R_{xx}\left( \frac{f_{s}}{f_{a}} \right)}} \end{matrix} \right.$

In this manner, the periodic nature of the noise is analyzed differently than the non-periodic nature of the desired signal.

To illustrate this, consider a high speed modem which samples the incoming signal at 9600 samples/second as described above. Referring to FIG. 2, there is shown a block diagram of a frequency estimation system in accordance with a preferred embodiment of the present invention. The input, x[k] is coupled to a first buffer 117, a first multiplier 118 and a second multiplier 122. The first buffer 117 is coupled to a second buffer 120 and to the first multiplier 118. The second buffer 120 is connected to the second multiplier 122. Additionally, there is a first summation block 124 which is connected to the first multiplier 118 and supplies the output for R_(xx)(160). There is also a second summation block 126 which is connected to the second multiplier 122 and supplies the output for R_(xx)(192).

In this embodiment, received samples of the signal x[k] are stored in buffers until 192 samples have been collected, as shown in FIG. 2. There is a first delay buffer 117, which is large enough for 160 samples, and a second delay buffer 120, which is large enough for 32 samples. In addition to the delay buffers, there are two multiplication blocks 118, 122 and two addition blocks 124, 126. In this manner, for the next 160(K) samples, as each new sample is received (sample k), it is multiplied by samples k-160 and k-192, and the products are added to the R_(xx)(160) and R_(xx)(192) totals. Only two multiplication and summing steps are required per sample, which is much less complex than other spectral analysis approaches. Other operations, apart from correlation, that show how well the current samples match the delayed samples may be used.

Although the foregoing discussion is addressed to the case wherein the periodic signal is labeled as noise, the periodic signal may be any type of electronic signal. Moreover, the comparison is not limited to two discrete frequencies but rather to any number of discrete frequencies. For example, if a finite range of frequencies for the interference signal is known (e.g., 50 to 55 Hz), each of the frequencies (50, 51, 52, 53, 54, and 55 Hz) can be compared to determine which of the five discrete frequencies is closest to the frequency of the periodic signal.

In another preferred embodiment of the invention, an apparatus and method for canceling noise in an electronic signal is provided. The apparatus may be referred to herein as an interference estimator. A system that will cancel such interference under these circumstances is shown in FIGS. 3a and 3 b.

The interference estimator does two things: it builds a model of the interference, and it provides samples of the model to be subtracted from the received signal that are in phase with and equal in amplitude to the interference component of the incoming signal. Source code for a preferred implementation of the interference estimator, written in DSP (assembly language) for the Texas Instruments (TI) TMS320C5x platform, is provided in Appendix B hereto.

To understand how the interference estimator cancels the interference, consider the feed-back system in FIG. 3a, wherein a buffer value is subtracted from the received sample, at the summation block 130, before being input into the interference estimator 128. The received signal r[k] consists of a desired signal, s[k], and periodic interference, n[k]. The received signal is input to a summation block 130 along with the output of the interference estimator, {circumflex over (n)}[k]. In practice, {circumflex over (n)}[k] is generated from the interference estimator 128, as described below, and is subtracted from r[k]. The output of the summation block is s [k]. As described subsequently with respect to FIG. 4, the interference estimator 128 includes a model of the interference. Based on the model, the interference estimator subtracts {circumflex over (n)}[k] (the model of the interference at sample k) from r[k] in order to generate ŝ[k].

Referring to FIG. 3b, there is shown a block diagram of a periodic interference cancellation system, which system is operable in a feed-forward mode, in an alternative embodiment of the invention. In this embodiment, the input to the interference estimator 132 is r[k], which is also supplied to the summation block 134. The output to the interference estimator 132 is subtracted from r[k] at summation block 124 to form ŝ[k].

By way of example, the frequency of this interference is exactly 60 Hz and the sample rate of the system is 6000 samples/sec. A circular buffer (b[k]) is created to model the noise in the system in order to determine {circumflex over (n)}[k], the actual model of the interference. For example, if interference model b[k] is perfectly in sync with the phase of the interference, which is described subsequently, b[k] represents {circumflex over (n)}[k]. If the model is out of phase with the interference, b[k] is corrected through interpolation to determine {circumflex over (n)}[k], the actual model of the interference.

Referring to FIG. 4, there is shown a block diagram of the signal integrator for generating the interference model b[k], in accordance with an embodiment of the present invention, for the interference estimator 128 as shown in FIG. 3a or the interference estimator 132 as shown in FIG. 3b. The signal x[k], which in the preferred embodiment is the received signal r[k], is input to a multiplication block 142 to be multiplied by α, a constant. The output of the multiplication block 142 and the output of a delay block 148 are input to a summation block 144. The delay block 148 delays whatever is input to the delay block for 100 samples in this example. The input to the second multiplication block 146 is the output of the delay block 148. The second multiplication block 146 multiplies the input by (1−α). The delay block 148 delays whatever is input to the delay block 148 for 100 samples in this example

As shown in FIG. 4, the circular buffer delay block 148 is 100 samples in length. As discussed above, if, for example, the sample rate of the system is 6000 samples/sec and the frequency of interference is exactly 60 Hz, then an integer number of samples can represent one cycle at the fundamental frequency of the interference. If, on the other hand, the frequency of interference is 50 Hz and the sample rate is 8000 samples/sec, the circular buffer will not represent one cycle at the fundamental frequency. Thus, depending on the sample rate and the frequency of interference, the circular buffer may also contain a fraction of the fundamental frequency or more than one cycle of the fundamental frequency. If the circular buffer does not equal one cycle of the fundamental frequency, values are adjusted using interpolation or other methods, as described subsequently.

Received samples are scaled by some factor alpha (0<α≦1), described subsequently, and integrated into the buffer as follows:

b[0]=(1−α)·b[ 0]+α·x[k]

b[1]=(1−α)·b[1]+α·x[k+1]

* * *

b[99]=(1−α)·b[99]+α·x[k+99]

The buffer then wraps around in the next cycle and recalculates the buffer as follows:

b[0]=(1−α)·b[0]+α·x[k+100]

b[1]=(1−α)·b[1]+α·x[k+101]

Because the signal s[k] is uncorrelated with itself, its contribution to the buffer will generally average to zero. The interference, on the other hand, is correlated at an interval equal to the length of the buffer (one cycle). Hence the buffer grows a model of one average cycle of the interference. Therefore, the interference is treated differently than the desired signal due to the correlated, periodic nature of the interference. And, the interference model treats the desired signal and the interference in the exact opposite manner as they are normally treated. Normally, it is the desired signal that is examined and the interference that is treated as background noise. However, the current interference model treats the interference as the primary signal for examination and the desired signal as background noise.

During the first time through the buffer (the first 100 received samples in this example), α=1 in a preferred embodiment. After the first time through the buffer, a can then be immediately set to a minimum value, or gradually reduced until it reaches the minimum value (e.g. letting a=1/(number of times through the buffer)). The larger the value of ax, the faster the buffer changes to reflect recent changes in the interference. A smaller α, on the other hand, builds a better average. The amplitude in either case will be the same as the average amplitude of the interference.

Likewise, the buffer for the feed-forward system, as shown in FIG. 3b, is as follows:

b[k mod 100]=(1−α)b[k mod 100]+α·x[k].

It has been assumed up to this point that that the frequency is fixed and that one interference cycle can be exactly represented by an integer number of samples; however, this may not always be the case. The frequency may drift, and the wavelength in samples may not be an integer number (as is the case where the circular buffer equals one cycle of the fundamental frequency). For example, while the average frequency for a power line may be 50 Hz or 60 Hz, the frequency varies over time by some degree. If this occurs, the received interference cycles will not “line up” as they are added into the buffer, and hence the buffer will not grow an average of the interference.

There are a couple of ways to handle this problem. In a preferred embodiment, the interference shift is monitored relative to the model, and then the received samples are interpolated in a manner such that one cycle will exactly fit into the buffer. Various methods, which are known in the art, may be utilized to perform the interpolation. In one embodiment, a linear interpolator provides sufficient estimation, and is shown for the model of the noise in the system, b[k] and for the actual model of the interference, n [k], in the following equations:

b[j]=b[j]+α*{a*x[k]+(1−a)*x[k−1]}

{circumflex over (n)}[k]=a*b[j]+(1−a)*b[j−1]

where a is a number between 0 and 1 which indicates where to interpolate the samples between x[k] and x[k−1].

Referring to FIG. 5, there is shown a block diagram for correlating the received signal with the interference model, as shown in FIG. 4, to determine phase offset. The signal x[k] is input to a multiplication block 150 which multiplies x[k] by α. The output of the multiplication block 150 is input to a summation block 152 along with the output of another multiplication block 154. The b[k] value output from summation block 152 is sent to three delay blocks 156, 158, 160 in order to delay the output value by 1, 98, and 1 samples, respectively. Further, the outputs of delay blocks 158, 160 are sent to multiplication blocks 162, 166, respectively, along with the signal x[k]. The outputs of the multiplication blocks 162, 166 are sent to a summation block 164, after which the sign of the phase offset is determined at 168. As described more fully below, the output of multiplication block 162 is x[k]*b[j−1] and the output of multiplication block 166 is x[k]*b[j+1]. These values are subtracted at summation block 164 to determine the value y[k]. The values of y[k] are then summed and the sign is determined at block 168.

FIG. 5 determines whether the phase is leading or lagging. In practice, if the phase is leading, the value of a, as used in the equations above for [b] and {circumflex over (n)}[k], is increased by 0.1 (this value may be modified based on the design choice); if the phase is lagging, the value of a is decreased by 0.1. In this manner, if a is previously zero, and the phase is leading, a is increased to 0.1. If on the next pass, the phase is still leading, a is again increased by 0.1 to 0.2. However, there may be instances where a more sophisticated interpolation method, such as a LaGrange interpolator, may be required.

Based on the phase of the system, the actual interference may lead, lag or be in sync with the model. If the phase is in sync, linear interpolation is not required. If the actual interference leads or lags the model, two interpolations are necessary. The first interpolation is to determine the “actual” x[k] in order to update the buffer model, b[k], as described in the following equation: b[j]=b[j]+α* {a*x[k]+(1−a)*x[k−1]}. For example, if the interference is lagging behind the model, then the “actual” x[k] is really in between x[k] and x[k−1]. Based on the amount of lag in the system, the “actual” x[k] is determined (which may then be used to update the interference model).

The second interpolation is to determine the “actual” b[j] in order to determine {circumflex over (n)}[k], as described by the following equation: {circumflex over (n)}[k]=a*b[j]+(1−a)*b[j−1]. Similar to calculating the “actual” x[k], {circumflex over (n)}[k] is modified based on whether the model is leading or lagging the interference.

In an alternative embodiment, the length of the buffer is made as close as possible to a length that represents an integer number of cycles. For example, if the sample rate is 8000 samples/second, a buffer length of 400 will exactly hold 3 cycles at exactly 60 Hz. Then, proceeding as described above, the system is monitored to determine if the received interference is drifting in phase relative to the model in the buffer. If the interference drifts by more than ½ of a sample, or ½ of whatever fraction of a sample the buffer can be broken down into, the buffer indices of the samples, into which the received samples are integrated, are shifted to put the received interference back in phase with the model. In practice, the pointer which addresses the specific entries within the buffer is incremented or decremented. Alternatively, the actual values in the buffer may be physically shifted to an adjacent buffer location (i.e., each of the buffer samples moved left or right) in order to effect the shift in buffer samples. (When more than one cycle is required to create a proper buffer, the different cycles in the buffer are out of phase with each other relative to the sample time by some fraction of a sample. Hence the precision to which one can identify a point on the model is that fraction.) In practice, the shifting of the indices is less accurate than the interpolation method described above.

In both of these cases (the interpolation and shifting methods), it is necessary to detect a shift of the interference phase relative to the model. This can be done by correlating the received interference with the model at various offsets. In the preferred embodiment, the offset is plus and minus one sample. The correlation value, Φ(n), where n is the offset, is then

Φ(1)=Σx[k]·b[j+1],

Φ(−1)=Σx[k]·b[j−1],

where x[k] is the current input sample to the estimator, b[j] is the current buffer sample, and the summation is over some number of input samples, the exact number of which is determined empirically. Preferably the summation is over 16 samples; however other numbers of samples, such as 8 or 32 samples may also be used. Therefore, the correlation shows how well the shifted model and the input signal are lined up in phase. Other operations, apart from correlation, that show how well the shifted model and the input signal are lined up in phase [or lined up with respect to another variable such as time] may be used.

The b[j] values are delayed using delay blocks of 1 and the buffer length —1, as shown by delay blocks 158, 160 (in the example shown in FIG. 5, the buffer length is 100). The b[j] values are then multiplied and summed to determine the sign of the offset. In FIG. 5, y[k] is calculated by subtracting x[k]·b[j+1] from x[k]·b[j−1], summed and the sign of the sum is determine. This is the same type of calculation as determining Φ(1), which is the summation of x[k]·b[j+1], and Φ(−1), which is the summation of x[k]·b[j−1], and comparing the two values Φ(1) and Φ(−1) to determine which one is larger.

If Φ(1)>Φ(−1), then the interference phase is lagging behind the model. If Φ(1)<Φ(−1), then the interference leads the model. If they are equal, then the interference is in phase with the model. In other words, FIG. 5 compares the buffer values with the incoming signal to determine if the phase is leading or lagging. The buffer is shifted forward for b[j+1] and correlated with x[k]. This value is Φ(1). The buffer is also shifted backward for b[j−1] and correlated with x[k]. This value is Φ(−1). Φ(1) and Φ(−1) therefore represent numbers to determine how well the buffer, whether b[j+1] or b[j−1] correlates. Based on the comparison of the two numbers, it may be determined whether the phase is leading or lagging.

In an alternative embodiment, one may calculate different offsets. For example, one may calculate Φ(2) and Φ(−2) if the phase is shifting quickly. Generally,

Φ(n)=Σx[k]·b[j+n]

for a different offset.

If the shifting method described above is used, it is useful to obtain a zero offset correlation value:

Φ(0)=Σx[k]·b[j],

so that if Φ(1)>Φ(0) the buffer index is advanced, if Φ(−1)>Φ(0) the buffer index is decremented, and if Φ(0)>Φ(1) & Φ(0)>Φ(−1) the buffer index is unchanged.

The final interference estimate sample to be subtracted from the next received sample is obtained by simply reading one sample ahead of the current buffer sample, if the shifting method is used. If the interpolation method is used, then another interpolation to calculate the “actual” b[j], as described above, must be done to obtain the estimate.

As discussed previously, in order to correct the phase of the system for the next sample, the model is adjusted based on whether the interference is lagging or leading the model. For example, if the interference is leading the model, the buffer is adjusted upward by 0.1 of a sample (this value may be modified based on the design choice); therefore, if on the next pass, the interference is still leading the model, the buffer is adjusted slightly upward again. Likewise, if the interference is lagging the model, the buffer is adjusted downward by 0.1 of a sample. This comprises a classical first order phase-locked loop. A classical second order phase-locked loop structure is implemented according to common practice in the code in Appendix B.

As indicated above, high speed modems are often subjected to periodic interference, or “hum.” This interference can cause a degradation of performance by creating decision errors in same manner of other forms of additive noise. To reduce the effects of this interference in any modem, and in particular to a pulse code modulation (PCM) modem, the interference canceller can be advantageously placed in the equalizer system as shown in FIG. 6a.

The received signal and the error term are input to a linear equalizer 170. The outputs of the linear equalizer 170, a decision feedback equalizer 174 and the interference estimator 180 are sent to a summation block 172. The output of the summation block is sent both to a decision block 176 and to another summation block 178. The output of the decision block 176 is also coupled to decision feedback equalizer 174.

An error term is generated at summation block 178, which error term is the difference between the equalizer output and the decision made on that output. The error term also is input to the decision feedback equalizer 174 and the linear equalizer 170. This error term, then, is used as the input to the interference estimator 180. The output of the interference estimator 180 is subtracted from the equalizer output at summation block 172.

When the line conditions are reasonably good, the error term will consist mostly of the periodic interference. The signal which is input to the interference estimator 180 is predominantly the noise signal so that the interference estimator 180 more quickly and accurately models the noise in the system. Signals that were input to the interference estimator in FIG. 4 were predominantly the desired signal with an additional noise signal. In those instances, since the noise signal was not predominant, more iterations are required to build the model for the interference estimator in order for the predominant desired signal to “average out” of the model. Regardless, any signal may be input to the interference estimator, as long as the signal includes the periodic noise.

Referring to FIG. 6b, there is shown a block diagram of the interference estimator as shown in FIG. 6a. The input waveform has a certain number of samples which defines one cycle of the waveform. According to one embodiment of the invention, the buffer, b[k], may be used to express that input waveform. The number of entries in the buffer b[k] can be set to any number, depending on the necessary accuracy for the interference cancellation. For example, the number of entries in the buffer may be an integer number for one cycle of the waveform (e.g., 100 samples for one cycle). Or, the number of entries in the buffer may result in a fraction of a number of samples for each cycle (e.g., 133 ⅓ samples for one cycle) for multi-cycle buffers. Because of interpolation, the number of samples for one cycle of the waveform need not be an integer number to define the waveform.

Referring to FIG. 6b, there is shown an error term, error[k]. This is the same term as shown in the output of the summation block 178 in FIG. 6a. As described previously, the interpolation equations for b[j] and {circumflex over (n)}[k] are the following: b[j]=b[j]+α*{a*x[k]+(1−a)*x[k−1]}; {circumflex over (n)}[k]=a*b[j]+(1−a)*b[j−1]. The error[k] value corresponds to x[k] value in the previous equation.

To calculate the b[j], error[k], and error[k−1], which is delayed by delay block 190, are input to a first interpolator 192. The first interpolator 192 includes two multiplication blocks 194, 196 and an addition block 198 and calculates the value of error[k]*(1−a)+error[k−1]*a. This value is input to multiplication block 200, and is multiplied by α. Block 204, which contains the buffer values, supplies b[j] at one output, which is input to the summation block 202. The output of the summation block 202 is then input to block 204 in order to update the buffer. Therefore, the value of b[j] is calculated using the equation b[j]+α*{a*x[k]+(1−a)*x[k−1]}.

In order to calculate {circumflex over (n)}[k], the output of block 204 is b[j]. Delay block 210 delays the output so that its output is b[j−1]. The two inputs, b[j] and b[j−1], are input to the second interpolator 212. b[j] is sent to multiplication block 214 and multiplied by a. b[j−1] is sent to multiplication block 216 and multiplied by 1−a. The two outputs are summed at summation block 218. The output, according to the equation outlined above is {circumflex over (n)}[k], which is sent to summation block 172, as shown in FIG. 6a.

The interference estimator 180 functions as described above with reference to FIGS. 3 through 5. However, as shown in FIG. 6b, there is no multiplication block 146 in order to multiply by (1−α), as was done in FIG. 4. The input to the delay block, as shown in FIG. 6a, is the error term. When first canceling the interference, the error term is large since the model has not had enough time to become an accurate model of the noise. As time passes, however, the model becomes more accurate. Because of this, the error term, which is the output of summation block 178, becomes smaller. Therefore, because the error term, which is input to the interference model, becomes smaller, there is no need to scale the output by 1−α.

In addition to corrupting data received by a high-speed modem, periodic interference may also prevent a modem's echo canceller from converging properly. During the echo canceller training phase, a modem requires that the only signal present on the phone line is echo from its own transmitted signal. If the echo canceller does not converge correctly due to hum on the line, performance is impaired. In this case, the periodic interference canceller can be used to subtract the hum from the received signal before the echo canceller, as shown in FIG. 7, receives it. The interference estimator 184, similar to FIG. 6b, generates {circumflex over (n)}[k] in order to cancel the noise within the system. Moreover, the adaptive filter 188 and delay 186 further generate ê[k] so that the output of the system is ŝ[k]. In a preferred embodiment, the interference is estimated and subtracted from the echo canceller during training mode. There may be two interference estimators, one for echo cancelling as shown in FIG. 7 and one for the data mode as shown in FIG. 6a.

It is intended that the foregoing detailed description be regarded as illustrative rather than limiting and that it is understood that the following claims, including all equivalents, are intended to define the scope of the invention.

APPENDIX A * To determine the frequency of the periodic interface, if there is any, * the buffer is first filled with arc_err_O samples (Stage 0). The error * signal can then be autocorrelated at an offset of one 60 Hz cycle and * one 50 Hz cycle (Stage 1). The frequency of the periodic interferences, * if any, will correspond to the larger correlation value. * Stage 0: load the buffer lacl h_stage ; check flag: this stage or next one? bcnd h_ec_stage1,NEQ lar ar0,#humbufstart+h_ec_long cmpr 0 ; equal ? (Stored one full cycle?) True:Tc=1 False:Tc=0 bcnd save_sample, NTC splk #humbufstart,hum_ptr lar ar1,hum_ptr add #1 ; set flag to start next stage sacl h_stage b h_ec_stage1 save_sample lacl h_err_0 sacl *+ ; store error in buffer, increment buffer index sar ar1,hum_ptr ; save new index b end_ec_humbucker h_ec_stage1 ;Stage 1:Correlate new received samples with samples in buffer sub #1 ; check flag: this stage or next one? bcnd start_ec_humbucker,NEQ lar ar0,#humnbufstart+h_ec_short cmpr 0 ; equal ? (Correlated one full cycle?) True:TC=1 False:TC=0 bcnd correlate_err,NTC splk #humbufstart,hum_ptr ; reset pointer add #2 sacl h_stage ; set flag to start next stage * make 50/60/nohum decision lar ar1,#arcflg apl #ahumbuck,* ; humbuck flag off splk #humbufstart+160,h_ec_len ; set 60 Hz buffer length splk #humbufstart+133,h_len lacc hc_50h,16 adds hc_50l sacb lacc hc_60h,16 adds hc_60l crgt ; 60 Hz correlation > 50 Hz correlation? bcnd check_hum_threshold,C ; If not, don't change buffer length. splk #humbufstart+192,h_ec_len ; Otherwise, set 50 Hz buffer length. splk #humbufstart+160,h_len check_hum_threshold lacc #hum_threshold,15 crgt ; Is there a hum? bcnd end_ec_humbucker,C ; If not, skip humbucker, and don't change * humbuck flag opl #ohumbuck,* ; Otherwise, set hum on flag. lacl #0 ; and initialize the humbucker sacl hum sacl h_vcol splk #H_ALPHAH,h_alpha splk #HC_LEN,hum_cnt b start_ec_humbucker correlate_err spm 0 lar ar0,#h_ec_long-h_ec_short lt h_err_0 mpy #0+ ; 50 Hz correlation lacc hc_50h,16 adds hc_50l mpya *0− ; 60 Hz correlation sach hc_50h sacl hc_50l lacc hc_60h,16 adds hc_60l apac sach hc_60h sacl hc_60l lacl #0 sacl #+ ; zero buffer, increment pointer sar ar1,hum_ptr spm 1 b end_ec_humbucker start_ec_humbucker * * Code in Appendix B, goes here. * end_ec_humbucker

APPENDIX B * - Cancels periodic interference mar *,ar1 lar ar1,#arcflg bit *,fhumbuck ; Is there any hum? bcnd end_humbucker,NTC ; If not, skip the humbucker lacl arc_err_0 ldp #4 dmov h_err_0 ; h_err_1 = h_err_0 sacl h_err_0 ; h_err_0 = receiver sample lar ar1,hum_ptr lacl nsphs ; nsphs = number (of equalizer output) * samples per hum sample sub #1 ; decrement nsphs sacl nsphs bcnd calculate_h_est,NEQ test_hum_ptr lar ar0,h_len cmpr 0 ; hum_ptr=(end of buffer)+1 ? True:TC=1 False:TC=0 bcnd interpolate_error,NTC rpt #2 bldd #humbufstart,*+ ; copy the first three buffer *  samples to the end of the buffer lar ar1,#humbuf start ;Pointer back to the beginning of the *  buffer lacc #h_gamma_min,15 sacb lacc h_gamma,15 sub h_gamma,12 ; exponential gamma reduction crgt ; Reduced gamma larger than min gamma? bcnd interpolate_error,NC ; If not, don't save the reduced value sach h_gamma,1 ; Otherwise, save it interpolate_error lacl hum ; old hum sacl h_tempx lt h_tap1 mpy h_err_0 pac lt h_tap2 mpy h_err_1 apac ; hum = h_err_0*h_tap1 + h_err_1*h_tap2 add h_one,14 ; correct for truncation sach hum,1 ; interpolated error term lar ar0,#2 lt hum mpy *0+ ; hum(t+0)*humbuffer(t−1) lacc hc,1 mpya *0− ; hum(t+0)*humbuffer(t+1) lts h_tempx ; tempx=old hum bsar 1 ; correct for shift in accumulation steps above, since pm=1 sacl hc ; cross-correlation *  hum(t+0)*humbuffer(t−1)−hum(t+0)*humbuffer(t+1) lacc *,15 mpy h_gamma apac ; acca=humbuffer + old hum * gamma add h_one,14 sach *+,1 ; store old interpolated error term in humbuffer sar ar1,hum_ptr ; store incremented pointer value update_h_vco lt h_int2 mpy #h_beta2 ; scale second order integrator output pac add h_vcoh,16 ; make timing adjustment adds h_vcol sach h_vcoh sacl h_vcol lacl h_gamma ; don't make loop corrections if the bcnd update_h_time,EQ ; humbucker is off lacc hum_cnt ; integrate/dump period over? sub #1 sacl hum_cnt bcnd update_h_time,NEQ ; no, continue integration splk #HC_LEN,hum_cnt ; yes, reload counter bit hc,b15 ; slice correlation difference sacl hc ; zero correlators lacc h_beta1,16 ; hum loop á1 xc 1,tc neg setc ovm ; update second order integrator add h_int2,16 ;  with ñ h_beta1 sach h_int2 clrc ovm lacc h_alpha ; hum loop à xc 1,tc neg add h_vcoh ; make first order correction update_h_time splk #0,h_vcoh ; (zero the correction) adds h_time ; make the correction, acch = −1,0,1 sacl h_time add #10h,12 ; calc # samples required for next baud sach nsphs ; nsphs = 0,1,2 lacl h_time ; h_time is between 0 and 65535 add h_one,1 bsar 2 ; h_tap1 is between 0 and 16383 sacl h_tap1 lacc h_one,14 sub h_tap1 sacl h_tap2 ; h_tap2 = 16384-h_tap1 lacl nsphs bcnd test_hum_ptr,EQ ; Do all this again if nsphs = 0 calculate_h_est lacl h_gamma bcnd end_humbucker,EQ ;Don't modify equalizer output if h_gamma=0 lacl #2 sub nsphs sacl h_tempx ; h_tempx = how many samples ahead in buffer to *   get estimate lar ar0,h_tempx mar #0+ lt h_tap1 mpy *+ pac lt h_tap2 mpy * apac ; interpolated hum estimate add h_one,14 neg ldp #6 add eq_outp,15 ; subtract hum estimate from equalizer output sach eq_outp,1 end_humbucker 

We claim:
 1. In a data communication device having a sampling rate and having an electronic signal containing a periodic signal, the periodic signal having a fundamental frequency, an interference estimator for modeling the periodic signal, the interference estimator comprising in combination: a buffer containing entries corresponding to at least one cycle at the fundamental frequency; a first multiplier coupled to receive the electronic signal; a delay block coupled to the buffer, the delay block being operable to delay the entries of the buffer an integer number of cycles of the fundamental frequency of the periodic signal; an adder coupled to the delay block and to the first multiplier, the adder adding the delayed buffer entries to the first multiplier output; and a second multiplier coupled between said delay block and said adder, wherein the first multiplier is not a constant value, and wherein the second multiplier is not a constant value.
 2. An interference estimator as claimed in claim 1, wherein an output of the adder is coupled to an input of the buffer.
 3. An interference estimator as claimed in claim 1, wherein the number of entries in the buffer equals the sampling rate divided by the fundamental frequency.
 4. An apparatus as claimed in claim 1, wherein, for at least a portion of time, the first multiplier and second multiplier have different values.
 5. An apparatus as claimed in claim 4, wherein the first multiplier is initially a different value than the second multiplier.
 6. An apparatus as claimed in claim 5, wherein the first multiplier is initially equal to 1 and the second multiplier is initially equal to
 0. 7. In a data communication device having a sampling rate and having an electronic signal containing a periodic signal, the periodic signal having a fundamental frequency, an interference estimator for modeling the periodic signal, the interference estimator comprising in combination: a buffer containing entries corresponding to at least one cycle at the fundamental frequency; a multiplier coupled to receive the electronic signal; a delay block coupled to the buffer, the delay block being operable to delay the entries of the buffer an integer number of cycles of the fundamental frequency of the periodic signal; an adder coupled to the delay block and to the multiplier, the adder adding the delayed buffer entries to the multiplier output; and a second multiplier coupled between said delay block and said adder, wherein the multiplier multiplies the electronic signal by a variable α and wherein the second multiplier multiplies the delayed buffer entries by a variable (1−α).
 8. In a data communication device having a sampling rate and having an electronic signal containing a periodic interference signal having a fundamental frequency, an apparatus for reducing the periodic interference signal in the electronic signal, the improvement comprising in combination: an interference estimator having a buffer containing entries corresponding to at least one cycle of the fundamental frequency, the entries modeling the periodic interference signal wherein the entries are comprised of samples of the electronic signals combined with samples of the electronic signals delayed an integer number of cycles of the fundamental frequency, wherein the interference estimator further comprises: a first multiplier coupled to the samples of the electronic signals, the first multiplier for multiplying the samples of electronic signals prior to being combined with the samples of the electronic signals delayed an integer number of cycles; and a second multiplier coupled to the samples of the electronic signals delayed an integer number of cycles, the second multiplier for multiplying the samples of the electronic signals delayed an integer number of cycles prior to being combined with the samples of the electronic signals, wherein the first multiplier initially multiplies with a first multiplier first value, wherein the first multiplier subsequently multiplies with a first multiplier second value, the first multiplier first value being different from the first multiplier second value, wherein the second multiplier initially multiplies with a second multiplier first value, and wherein the second multiplier subsequently multiplies with a second multiplier second value, the second multiplier first value being different from the second multiplier second value.
 9. An apparatus as claimed in claim 8, wherein the first multiplier multiplies the samples of the electronic signals by α and wherein the second multiplier multiplies the samples of the electronic signals delayed an integer number of cycles by (1−α).
 10. An apparatus as claimed in claim 8, wherein the first multiplier first value multiplies the samples for at least one cycle of the fundamental frequency, wherein the first multiplier second value multiplies the samples for at least one cycle of the fundamental frequency, wherein the second multiplier first value multiplies for at least one cycle of the fundamental frequency, and wherein the second multiplier second value multiplies for at least one cycle of the fundamental frequency.
 11. A method as claimed in claim 10, wherein the first multiplier first value is equal to one, and wherein the second multiplier first value is equal to zero.
 12. A method as claimed in claim 11, wherein the first multiplier second value is equal to a variable α, and wherein the second multiplier second value is equal to 1−α.
 13. A method for modeling periodic noise within an electronic signal, the method comprising the steps of: selecting a frequency for the periodic noise; filling a buffer with a first set of samples of the electronic signal; delaying the first set of samples in the buffer for an integer number of cycles of the frequency of the periodic noise to generate a second set of samples; adding the first set of samples with the second set of samples; replacing the first set of samples in the buffer with the sum of the first set of samples and the second set of samples; and scaling the first set of samples of the electronic signal with a first scale factor, wherein the step of filling a buffer includes filling the buffer with the scaled first set of samples, further comprising the step of scaling the second set of samples of the electronic signal with a second scale factor, and wherein the step of adding the first set of samples to the second set of samples includes adding the first set of samples scaled with the first scale factor to the second set of samples scaled with the second scale factor, wherein the first scale factor is a variable α and wherein the second scale factor is (1−α).
 14. A method for modeling periodic noise within an electronic signal, the method comprising the steps of: selecting a frequency for the periodic noise; filling a buffer with a first set of samples of the electronic signal; delaying the first set of samples in the buffer for an integer number of cycles of the frequency of the periodic noise; adding the first set of samples in the buffer with a second set of samples, the second set of samples being an integer number of cycles of the frequency of the periodic noise from the first set of samples; replacing the first set of samples in the buffer with the sum of the first set of samples and the second set of samples; and determining whether the buffer lags, leads or is in sync with the periodic noise, wherein the step of determining whether the buffer lags, leads or is in sync with the periodic noise includes correlating the periodic noise with the buffer entries at different offsets.
 15. A method as claimed in claim 14, further comprising the step of interpolating the electronic signals when the buffer lags or leads the periodic noise.
 16. A method for modeling periodic noise in an electronic signal, the electronic signal also including a non-correlated desired signal, the method comprising the steps of: creating a buffer having entries; and iteratively filling the buffer entries with values based on scaled samples of the electronic signal at points within the cycle of the fundamental frequency for the periodic noise and values based on delayed samples, thereby treating the desired signal as background noise by averaging out the desired signal from the values entered in the buffer, wherein the samples of the electronic signal are scaled by a variable α, wherein α is initially equal to 1 and thereafter is changed to less than
 1. 17. A method as claimed in claim 16, wherein, after the variable α is initially equal to 1, the variable α is equal to 1/(number of times iteratively filling the buffer).
 18. A method for modeling periodic noise in an electronic signal, the electronic signal also including a non-correlated desired signal, the method comprising the steps of: creating a buffer having entries; and iteratively filling the buffer entries with values based on scaled samples of the electronic signal at points within the cycle of the fundamental frequency for the periodic noise and values based on delayed samples, thereby treating the desired signal as background noise by averaging out the desired signal from the values entered in the buffer, wherein the samples of the electronic signal are scaled by a variable α and delayed samples are scaled by a variable (1−α).
 19. In a device that functions as a modem connected to a telephone network, an equalizer system for reducing periodic noise having a frequency, comprising: a linear equalizer, the linear equalizer having as one input a received signal; a first summation block, the summation block connected to the linear equalizer; a decision block, the output of the first summation block being input to the decision block; a second summation block, the output of which is an error term, the output of the first summation block and the output of the decision block being input to the second summation block, the error term being a subtraction of the output of the decision block from the output of the first summation block, the error term also being input to the linear equalizer; a decision feedback equalizer, the output of the decision block being input to the decision feedback equalizer, the output of the second summation block being input to the decision feedback equalizer, the output of the decision feedback equalizer being input to the first summation block; and an interference estimator, the output of the second summation block being input to the interference estimator, the output of the interference estimator being input to the first summation block wherein the interference estimator output is subtracted from the addition of linear equalizer output and the decision feedback equalizer output, wherein the interference estimator comprises: a multiplier for scaling the error term input with a scaled factor; a buffer containing entries corresponding to at least one cycle of the frequency of the periodic noise; means for delaying the buffer entries an integer number of cycles of the frequency of the periodic signal; and means for adding the delayed buffer entries to the scaled error term to update the buffer entries.
 20. In a device that functions as a modem connected to a telephone network, an equalizer system for reducing periodic noise having a frequency, comprising: a linear equalizer, the linear equalizer having as one input a received signal; a first summation block, the summation block connected to the linear equalizer; a decision block, the output of the first summation block being input to the decision block; a second summation block, the output of which is an error term, the output of the first summation block and the output of the decision block being input to the second summation block, the error term being a subtraction of the output of the decision block from the output of the first summation block, the error term also being input to the linear equalizer; a decision feedback equalizer, the output of the decision block being input to the decision feedback equalizer, the output of the second summation block being input to the decision feedback equalizer, the output of the decision feedback equalizer being input to the first summation block; and an interference estimator, the output of the second summation block being input to the interference estimator, the output of the interference estimator being input to the first summation block wherein the interference estimator output is subtracted from the addition of linear equalizer output and the decision feedback equalizer output, wherein the interference estimator further comprises: a first interpolator, the first interpolator having as an input the error term, the output of the first interpolator being input to a multiplier; and a second interpolator, the second interpolator having as an input a buffer, the output of the second interpolator being input to the first summation block.
 21. In a modem connected to a telephone network and having a transmitted signal, an echo canceling system for reducing the signal associated with periodic noise having a frequency, the echo canceling system comprising: a summation block; an electronic signal input to the summation block; an interference estimator, the output of the summation block being input to the interference estimator, the output of the interference estimator being input to the summation block, the interference estimator comprising a multiplier for scaling the input to the interference estimator with a scaled factor, a buffer containing entries corresponding to at least one cycle of the frequency of the periodic noise, a delay block for delaying the buffer entries an integer number of cycles of the frequency of the periodic signal; and an adder coupled to the delay block for adding the buffer entries to the scaled input in order to update the circular buffer entries; an adaptive filter, the adaptive filter having as inputs the output of the summation block and the transmitted signal; and a delay block, the delay block having as an input the output of the adaptive filter, wherein the output of the delay block and interference estimator is subtracted from the electronic signal.
 22. In a modem connected to a telephone network and having a transmitted signal, an echo canceling system for reducing the signal associated with periodic noise having a frequency, the echo canceling system comprising: a summation block; an electronic signal input to the summation block: an interference estimator, the output of the summation block being input to the interference estimator, the output of the interference estimator being input to the summation block, the interference estimator comprising a first interpolator having an input and an output, the input of the first interpolator being coupled to the output of the summation block and the output of the first interpolator being coupled to a multiplier; the multiplier scaling the output of the first interpolator with a scaled factor to generate a scaled signal, a buffer containing entries for receiving the scaled signal, the buffer having an output; an adder coupled to the buffer for adding the buffer output to the scaled signal in order to update the buffer entries, and a second interpolator having an input and an output, the input of the second interpolator coupled to the buffer output and the output of the second interpolator coupled to the input of the summation block; an adaptive filter, the adaptive filter having as inputs the output of the summation block and the transmitted signal; and a delay block, the delay block having as an input the adaptive filter, wherein the output of the delay block and interference estimator is subtracted from the electronic signal.
 23. A method of reducing periodic interference in an electronic signal, comprising the steps of: determining a period for the periodic interference; obtaining samples of the electronic signal; generating a model of the periodic interference; determining whether the model of the periodic interference leads, lags or is in sync with the periodic interference; correcting the model based on the determination of whether the model leads, lags or is in sync with the periodic interference; and applying the model for the periodic interference to the electronic signal, thereby reducing the periodic interference in the electronic signal.
 24. A method as claimed in claim 23, wherein the leading or lagging of the model of the periodic interference with the periodic interference is due to a drift in phase of the periodic interference relative to the model.
 25. A method as claimed in claim 23, wherein the leading or lagging of the model of the periodic interference with the periodic interference is due to a change in frequency of the periodic interference.
 26. A method as claimed in claim 23, wherein the step of determining whether he model of the periodic interference leads, lags or is in sync with the periodic interference includes correlating the periodic interference at offsets within the model.
 27. A method as claimed in claim 26, wherein the correlating of the periodic interference at offsets within the model includes calculating the following: Φ(1)=Σx[k]·b[j+1], Φ(−1)=Σx[k]·b[j−1], where x[k] is a current electronic signal, b[j] is a current buffer sample, and the summation is over a predetermined number of samples.
 28. A method as claimed in claim 23, wherein the model includes discrete entries in a buffer and wherein the step correcting the model based on the determination of whether the model leads, lags or is in sync with the periodic interference includes interpolating the buffer entries.
 29. A method as claimed in claim 23, wherein the model includes discrete entries in a buffer and wherein the step of correcting the model based on the determination of whether the model leads, lags or is in sync with the periodic interference includes shifting the entries in the buffer when the buffer entries lag or lead the phase of the periodic noise.
 30. A method as claimed in claim 29, wherein a pointer addresses entries in the buffer and wherein the shifting of entries occurs based on moving the pointer to a different entry in the buffer. 